By L. Huang
This up-to-date moment variation broadens the reason of rotational kinematics and dynamics — crucial element of inflexible physique movement in 3-dimensional house and a subject matter of a lot higher complexity than linear movement. It expands therapy of vector and matrix, and contains quaternion operations to explain and research inflexible physique movement that are present in robotic regulate, trajectory making plans, 3D imaginative and prescient procedure calibration, and hand-eye coordination of robots in meeting paintings, and so forth. It positive factors up to date remedies of techniques in all chapters and case studies.
The textbook keeps its comprehensiveness in assurance and compactness in measurement, which make it simply obtainable to the readers from multidisciplinary components who are looking to clutch the major thoughts of inflexible physique mechanics that are often scattered in a number of volumes of conventional textbooks. Theoretical suggestions are defined via examples taken from throughout engineering disciplines and hyperlinks to functions and extra complicated classes (e.g. commercial robotics) are provided.
Ideal for college kids and practitioners, this ebook presents readers with a transparent route to figuring out inflexible physique mechanics and its value in several sub-fields of mechanical engineering and comparable areas.
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Additional info for A Concise Introduction to Mechanics of Rigid Bodies: Multidisciplinary Engineering
It meets all the requirements of a rotation matrix, and it becomes a basic O of fUg. Â/ by a geometric analysis, as shown in Fig. 7. In a plane perpendicular to rO at N, Q moves to P under the rotation around rO with angle Â. The vectors and 0 are formed from O in rO to the points Q and P. From P, draw a line perpendicular to NQ and meets the latter at the point V. The relationship between and 0 is related to the orientation produced by the rotation. From the figure, it is obvious that 0 ! ! 9) There exist the following relations among the vectors at the right-hand side of the above equation, and the other vector ON in the figure is the projection of onto rO , and NV is the projection of NP onto NQ D ON.
10 shows one type of sequence of rotations in which the body of the frame fBg represented by the axes xO 000 O 000 O000 B, y B , and z B is produced from frame fAg by rotations 0 around the axes zOA (angle ˛), yO B (angle ˇ), and xO 00B (angle ) consecutively. The Euler angles ˛, ˇ, and are called Z Y X Euler angles, corresponding to the yaw, pitch, and roll angles usually used in practice. From the definition of basic rotation matrices and the formula to derive the orientation of a body from successive rotations in Sect.
In this example, the rotational axis zA D Œ0 0 1T and the rotational angle Â are given. 41). 45) 0 sin Â cos Â sin Â 0 cos Â 52 2 Orientation and Position Representation Fig. 3. As schematically shown in Fig. 15, a mechanism consists of a rod (OA OB ) and a rectangular box (EFGH). 2 about the joint axis with the rod, xB , which goes through the center of the box. The dimensions of the rod and the box are shown in the figure. Our task is to determine the positions and orientation of all the rigid bodies, given the angular displacements of the rod and the box about their rotation axes respectively.
A Concise Introduction to Mechanics of Rigid Bodies: Multidisciplinary Engineering by L. Huang